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Pulsating pure-quartic solitons with spectral asymmetry in an ultrafast fiber laser 超快光纤激光器中具有谱不对称的脉冲纯四次孤子
IF 5.6 1区 数学
Chaos Solitons & Fractals Pub Date : 2025-09-03 DOI: 10.1016/j.chaos.2025.117169
Yingjie Lin , Yanxin Liu , Yufeng Song , Zhixiang Deng , Zhenhong Wang , Jun Liu , Chunxiang Zhang , Pinghua Tang
{"title":"Pulsating pure-quartic solitons with spectral asymmetry in an ultrafast fiber laser","authors":"Yingjie Lin ,&nbsp;Yanxin Liu ,&nbsp;Yufeng Song ,&nbsp;Zhixiang Deng ,&nbsp;Zhenhong Wang ,&nbsp;Jun Liu ,&nbsp;Chunxiang Zhang ,&nbsp;Pinghua Tang","doi":"10.1016/j.chaos.2025.117169","DOIUrl":"10.1016/j.chaos.2025.117169","url":null,"abstract":"<div><div>In this work, we report the first experimental generation and observation of pure-quartic soliton (PQS) pulsations with spectral asymmetry in an ultrafast fiber laser. In addition to the asymmetric spectral sidebands, a unique feature of these observed pulsating PQSs lies in that the pulsation periods are fairly stable for varying net fourth-order dispersion (FOD) values and pump powers. Moreover, the pulsating PQSs exhibit a maximum average output power of ~22.16 mW, corresponding to a pulse energy of ~2.34 nJ. Finally, numerical simulations have been performed, which are in good agreement with the experimental results. These findings not only reveal a new dynamic regime of PQSs but also provide critical insights into the underlying mechanisms governing their formation and stability, further laying a foundational framework for the future development of high-energy PQS fiber lasers and contributing to a broader understanding of soliton dynamics driven by higher-order dispersion effects.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117169"},"PeriodicalIF":5.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144987940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stokes-Brinkman equations with diffusion and convection in thin tube structures 薄管结构中扩散和对流的Stokes-Brinkman方程
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-03 DOI: 10.1016/j.jde.2025.113728
Antonio Gaudiello , Grigory Panasenko
{"title":"Stokes-Brinkman equations with diffusion and convection in thin tube structures","authors":"Antonio Gaudiello ,&nbsp;Grigory Panasenko","doi":"10.1016/j.jde.2025.113728","DOIUrl":"10.1016/j.jde.2025.113728","url":null,"abstract":"<div><div>The steady state Stokes-Brinkman equations coupled with a system of diffusion-convection equations in a thin tube structure is considered. The Brinkman term differs from zero only in small balls near the ends of the tubes. The boundary conditions are: given pressure and concentrations at the inflow and outflow of the tube structure, the no slip boundary condition on the lateral boundary for the fluid, and Neumann type condition on the lateral boundary for the diffusion-convection equations. In this paper, the existence, uniqueness, and stability of the solution to such a problem are proved. Moreover, some <em>a priori</em> norm-estimates depending on the small thickness of the tubes are also provided. This model is well suited to describing thrombosis in blood vessels.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"450 ","pages":"Article 113728"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The right-sided quaternionic free metaplectic transformation and associated uncertainty principles 右四元数自由变形及相关的测不准原理
IF 1.6 3区 数学
Analysis and Mathematical Physics Pub Date : 2025-09-03 DOI: 10.1007/s13324-025-01125-y
Khaled Hleili, Youssef El Haoui
{"title":"The right-sided quaternionic free metaplectic transformation and associated uncertainty principles","authors":"Khaled Hleili,&nbsp;Youssef El Haoui","doi":"10.1007/s13324-025-01125-y","DOIUrl":"10.1007/s13324-025-01125-y","url":null,"abstract":"<div><p>The aim of this paper is to investigate the right-sided quaternionic free metaplectic transformation (QFMT) and its associated uncertainty principles (UPs) for <span>(mathbb {R}^{2d})</span>-dimensional quaternionic-valued signals. First, we establish the fundamental mathematical properties of the QFMT, including partial derivatives, the inversion formula, Parseval’s theorem, and the Hausdorff–Young inequality. Next, we establish various UPs within this framework, such as the Rènyi and Shannon entropy UPs and Donoho–Stark’s UP in terms of concentration. Finally, we derive <span>(L^a)</span>-bandlimited variant of the Donoho–Stark UP in the QFMT domain.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 5","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dichotomy laws for the Hausdorff measure of shrinking target sets in β $beta$ -dynamical systems β $ β $ -动力系统中收缩目标集的Hausdorff测度的二分律
IF 1.2 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-03 DOI: 10.1112/jlms.70284
Yubin He
{"title":"Dichotomy laws for the Hausdorff measure of shrinking target sets in \u0000 \u0000 β\u0000 $beta$\u0000 -dynamical systems","authors":"Yubin He","doi":"10.1112/jlms.70284","DOIUrl":"https://doi.org/10.1112/jlms.70284","url":null,"abstract":"<p>In this paper, we investigate the Hausdorff measure of shrinking target sets in <span></span><math>\u0000 <semantics>\u0000 <mi>β</mi>\u0000 <annotation>$beta$</annotation>\u0000 </semantics></math>-dynamical systems. These sets are dynamically defined in analogy to the classical theory of weighted and multiplicative Diophantine approximation. While the Lebesgue measure and Hausdorff dimension theories for these sets are well-understood, much remains unknown about the Hausdorff measure theory. We show that the Hausdorff measure of these sets is either zero or full depending upon the convergence or divergence of a certain series, thus providing a rather complete measure theoretic description of these sets.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Concave foliated flag structures and the SL3(R) Hitchin component 凹叶面旗结构和SL3(R) Hitchin分量
IF 1.5 1区 数学
Advances in Mathematics Pub Date : 2025-09-03 DOI: 10.1016/j.aim.2025.110504
Alexander Nolte, J. Maxwell Riestenberg
{"title":"Concave foliated flag structures and the SL3(R) Hitchin component","authors":"Alexander Nolte,&nbsp;J. Maxwell Riestenberg","doi":"10.1016/j.aim.2025.110504","DOIUrl":"10.1016/j.aim.2025.110504","url":null,"abstract":"<div><div>We give a geometric characterization of flag geometries associated to Hitchin representations in <span><math><msub><mrow><mi>SL</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>. Our characterization is based on distinguished invariant foliations, similar to those studied by Guichard-Wienhard in <span><math><msub><mrow><mi>PSL</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span>.</div><div>We connect to the dynamics of Hitchin representations by constructing refraction flows for all positive roots in general <span><math><msub><mrow><mi>sl</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>R</mi><mo>)</mo></math></span> in our setting. One consequence is that the highest root flows are <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>α</mi></mrow></msup></math></span>. For <span><math><mi>n</mi><mo>=</mo><mn>3</mn></math></span>, leaves of our one-dimensional foliations are flow-lines.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"480 ","pages":"Article 110504"},"PeriodicalIF":1.5,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The long-wave–short-wave resonance interaction model: Generalized higher-order semi-rational rogue wave solutions and their dynamics 长波-短波共振相互作用模型：广义高阶半有理异常波解及其动力学
IF 5.6 1区 数学
Chaos Solitons & Fractals Pub Date : 2025-09-03 DOI: 10.1016/j.chaos.2025.117133
Jiguang Rao , T. Kanna , Jingsong He
{"title":"The long-wave–short-wave resonance interaction model: Generalized higher-order semi-rational rogue wave solutions and their dynamics","authors":"Jiguang Rao ,&nbsp;T. Kanna ,&nbsp;Jingsong He","doi":"10.1016/j.chaos.2025.117133","DOIUrl":"10.1016/j.chaos.2025.117133","url":null,"abstract":"<div><div>By utilizing the bilinear Kadomtsev–Petviashvili (KP) hierarchy reduction approach, a class of generalized higher-order semi-rational rogue wave solutions to the long-wave–short-wave resonance interaction model is constructed. These solutions are expressed through a combination of Schur polynomials and exponential terms, and they characterize complex nonlinear excitations involving a superposition of three types of waves: bounded rogue waves of order <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, breather waves of order <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and dark solitons of order <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>, where <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> are arbitrary nonnegative integers. Within this bilinear formalism, we demonstrate that several special cases, including purely rational rogue wave configurations, pure breather states, isolated dark solitons, and their hybrid combinations, can be retrieved by suitably choosing the values of these parameters. A significant advancement of our current KP hierarchy reduction scheme, in contrast to previous bilinear techniques for solving one-dimensional (1D) integrable equations, lies in the adoption of a generalized tau function representation that seamlessly accommodates different types of solitary waves. This flexible structure not only unifies various known solutions but also enables the study of semi-rational rogue wave dynamics across a broader class of 1D integrable systems. Furthermore, it allows for the exploration of rich dynamics associated with rogue waves riding on backgrounds formed by breathers, dark solitons, or their combinations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117133"},"PeriodicalIF":5.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric realizations of the s-weak order and its lattice quotients s-弱阶及其格商的几何实现
IF 1.2 2区 数学
Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-03 DOI: 10.1112/jlms.70268
Eva Philippe, Vincent Pilaud
{"title":"Geometric realizations of the s-weak order and its lattice quotients","authors":"Eva Philippe,&nbsp;Vincent Pilaud","doi":"10.1112/jlms.70268","DOIUrl":"https://doi.org/10.1112/jlms.70268","url":null,"abstract":"<p>For an <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-tuple <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math> of nonnegative integers, the <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math>-weak order is a lattice structure on <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math>-trees, generalizing the weak order on permutations. We first describe the join irreducible elements, the canonical join representations, and the forcing order of the <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math>-weak order in terms of combinatorial objects, generalizing the arcs, the noncrossing arc diagrams, and the subarc order for the weak order. We then extend the theory of shards and shard polytopes to construct geometric realizations of the <span></span><math>\u0000 <semantics>\u0000 <mi>s</mi>\u0000 <annotation>${bm{s}}$</annotation>\u0000 </semantics></math>-weak order and all its lattice quotients as polyhedral complexes, generalizing the quotient fans and quotientopes of the weak order.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70268","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Noetherianity of polynomial rings up to group actions 多项式的noether性适用于群行为
IF 0.8 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2025-09-03 DOI: 10.1016/j.jpaa.2025.108081
Liping Li , Yinhe Peng , Zhengjun Yuan
{"title":"Noetherianity of polynomial rings up to group actions","authors":"Liping Li ,&nbsp;Yinhe Peng ,&nbsp;Zhengjun Yuan","doi":"10.1016/j.jpaa.2025.108081","DOIUrl":"10.1016/j.jpaa.2025.108081","url":null,"abstract":"<div><div>Let <em>k</em> be a commutative Noetherian ring, and <span><math><mi>k</mi><mo>[</mo><mi>S</mi><mo>]</mo></math></span> the polynomial ring whose indeterminates are parameterized by elements in a set <em>S</em>. We show that <span><math><mi>k</mi><mo>[</mo><mi>S</mi><mo>]</mo></math></span> is Noetherian up to highly homogenous actions of groups. In particular, there is a special linear order ⩽ on infinite <em>S</em> such that <span><math><mi>k</mi><mo>[</mo><mi>S</mi><mo>]</mo></math></span> is Noetherian up to actions of <span><math><mi>Aut</mi><mo>(</mo><mi>S</mi><mo>,</mo><mo>⩽</mo><mo>)</mo></math></span>, and the existence of such a linear order for every infinite set is equivalent to the axiom of choice. These Noetherian results are proved via a sheaf theoretic approach based on Artin's theorem, the work of Nagel-Römer in <span><span>[21]</span></span>, and a classification of highly homogenous groups by Cameron in <span><span>[6]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 10","pages":"Article 108081"},"PeriodicalIF":0.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996519","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Localized seeding for triggering the global social contagion in higher-order spatial networks 高阶空间网络中触发全球社会传染的局部播种
IF 5.6 1区 数学
Chaos Solitons & Fractals Pub Date : 2025-09-03 DOI: 10.1016/j.chaos.2025.117141
Anbin Liu , Dayong Xiao , Wenjie Li , Tao Yang , Chun Yang , Jie Fan , Wei Wang
{"title":"Localized seeding for triggering the global social contagion in higher-order spatial networks","authors":"Anbin Liu ,&nbsp;Dayong Xiao ,&nbsp;Wenjie Li ,&nbsp;Tao Yang ,&nbsp;Chun Yang ,&nbsp;Jie Fan ,&nbsp;Wei Wang","doi":"10.1016/j.chaos.2025.117141","DOIUrl":"10.1016/j.chaos.2025.117141","url":null,"abstract":"<div><div>Extensive research has explored the contagion dynamics of social behaviors on higher-order spatial networks and uncovered many important findings, most of which are based on random seed strategies. In this study, we propose a social contagion model on higher-order spatial networks driven by local seeds, examining the impact of the network’s spatial structure on contagion modes and speeds. Previous research has suggested that clustered networks are more conducive to the diffusion of behavior. However, we find that excessively clustered networks inhibit behavior spread under local seed strategies. In highly clustered networks, individuals experience stronger social reinforcement; however, this also creates redundant connections, causing contagion to remain localized and preventing it from spreading over longer distances. Therefore, behavior diffusion is most effective when the network structure strikes a balance between social reinforcement and spatial distance, thus maximizing the synergy between low- and higher-order contagion.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"200 ","pages":"Article 117141"},"PeriodicalIF":5.6,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions 具有周期边界条件的五阶修正KdV型方程的消去性质和无条件适定性
IF 2.3 2区 数学
Journal of Differential Equations Pub Date : 2025-09-03 DOI: 10.1016/j.jde.2025.113736
Takamori Kato , Kotaro Tsugawa
{"title":"Cancellation properties and unconditional well-posedness for fifth order modified KdV type equations with periodic boundary conditions","authors":"Takamori Kato ,&nbsp;Kotaro Tsugawa","doi":"10.1016/j.jde.2025.113736","DOIUrl":"10.1016/j.jde.2025.113736","url":null,"abstract":"<div><div>We prove the unconditional well-posedness result for fifth order modified KdV type equations in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>(</mo><mi>T</mi><mo>)</mo></math></span> when <span><math><mi>s</mi><mo>≥</mo><mn>3</mn><mo>/</mo><mn>2</mn></math></span>, which includes non-integrable cases. By the conservation laws, we also obtain the global well-posedness result when <span><math><mi>s</mi><mo>=</mo><mn>2</mn></math></span>, which also includes non-integrable cases. The main idea is to employ the normal form reduction and a kind of cancellation properties to deal with the derivative losses.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"450 ","pages":"Article 113736"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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